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Diff for /OpenXM/src/asir-doc/parts/ff.texi between version 1.3 and 1.4

version 1.3, 2000/01/13 08:29:56 version 1.4, 2003/04/19 10:36:30
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/ff.texi,v 1.2 1999/12/21 02:47:31 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/ff.texi,v 1.3 2000/01/13 08:29:56 noro Exp $
 \BJP  \BJP
 @node $BM-8BBN$K4X$9$k1i;;(B,,, Top  @node $BM-8BBN$K4X$9$k1i;;(B,,, Top
 @chapter $BM-8BBN$K4X$9$k1i;;(B  @chapter $BM-8BBN$K4X$9$k1i;;(B
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Line 34 
   
 @noindent  @noindent
 \BJP  \BJP
 @b{Asir} $B$K$*$$$F$O(B, $BM-8BBN$O(B, $B@5I8?tAGBN(B GF(p), $BI8?t(B 2 $B$NM-8BBN(B GF(2^n)  @b{Asir} $B$K$*$$$F$O(B, $BM-8BBN$O(B, $B@5I8?tAGBN(B GF(p), $BI8?t(B 2 $B$NM-8BBN(B GF(2^n),
   GF(p) $B$N(B n $B<!3HBg(B GF(p^n)
 $B$,Dj5A$G$-$k(B. $B$3$l$i$OA4$F(B, @code{setmod_ff()} $B$K$h$jDj5A$5$l$k(B.  $B$,Dj5A$G$-$k(B. $B$3$l$i$OA4$F(B, @code{setmod_ff()} $B$K$h$jDj5A$5$l$k(B.
 \E  \E
 \BEG  \BEG
 On @b{Asir} @var{GF(p)} and @var{GF(2^n)} can be defined, where  On @b{Asir} @var{GF(p)}, @var{GF(2^n)}, @var{GF(p^n} can be defined, where
 @var{GF(p)} is a finite prime field of charateristic @var{p} and  @var{GF(p)} is a finite prime field of charateristic @var{p},
 @var{GF(2^n)} is a finite field of characteristic 2. These are  @var{GF(2^n)} is a finite field of characteristic 2 and
   @var{GF(p^n} is a finite extension of @var{GF(p)}. These are
 all defined by @code{setmod_ff()}.  all defined by @code{setmod_ff()}.
 \E  \E
   
Line 59  x^50+x^4+x^3+x^2+1
Line 61  x^50+x^4+x^3+x^2+1
 x^50+x^4+x^3+x^2+1  x^50+x^4+x^3+x^2+1
 [6] field_type_ff();  [6] field_type_ff();
 2  2
   [7] setmod_ff(x^3+x+1,1125899906842679);
   [1*x^3+1*x+1,1125899906842679]
   [8] field_type_ff();
   3
   [9] setmod_ff(3,5);
   [3,x^5+2*x+1,x]
   [10] field_type_ff();
   4
 @end example  @end example
 \BJP  \BJP
 @code{setmod_ff()} $B$O(B, $B0z?t$,@5@0?t(B p $B$N>l9g(B GF(p), n $B<!B?9`<0(B f(x) $B$N>l(B  @code{setmod_ff()} $B$O(B, $B$5$^$6$^$J%?%$%W$NM-8BBN$r4pACBN$H$7$F%;%C%H$9$k(B.
   $B0z?t$,@5@0?t(B p $B$N>l9g(B GF(p), n $B<!B?9`<0(B f(x) $B$N>l(B
 $B9g(B, f(x) mod 2 $B$rDj5AB?9`<0$H$9$k(B GF(2^n) $B$r$=$l$>$l4pACBN$H$7$F%;%C%H$9(B  $B9g(B, f(x) mod 2 $B$rDj5AB?9`<0$H$9$k(B GF(2^n) $B$r$=$l$>$l4pACBN$H$7$F%;%C%H$9(B
 $B$k(B. @code{setmod_ff()} $B$K$*$$$F$O0z?t$N4{Ls%A%'%C%/$O9T$o$:(B, $B8F$S=P$7B&(B  $B$k(B. $B$^$?(B, $BM-8BAGBN$NM-8B<!3HBg$bDj5A$G$-$k(B. $B>\$7$/$O(B @xref{$B?t$N7?(B}.
   @code{setmod_ff()} $B$K$*$$$F$O0z?t$N4{Ls%A%'%C%/$O9T$o$:(B, $B8F$S=P$7B&(B
 $B$,@UG$$r;}$D(B.  $B$,@UG$$r;}$D(B.
   
 $B4pACBN$H$O(B, $B$"$/$^$GM-8BBN$N85$H$7$F@k8@$"$k$$$ODj5A$5$l$?%*%V%8%'%/%H$,(B,  $B4pACBN$H$O(B, $B$"$/$^$GM-8BBN$N85$H$7$F@k8@$"$k$$$ODj5A$5$l$?%*%V%8%'%/%H$,(B,
Line 87  If @var{f} is a univariate polynomial of degree @var{n
Line 99  If @var{f} is a univariate polynomial of degree @var{n
 @code{setmod_ff(@var{f})} sets @var{GF(2^n)} as the current  @code{setmod_ff(@var{f})} sets @var{GF(2^n)} as the current
 base field.  @var{GF(2^n)} is represented  base field.  @var{GF(2^n)} is represented
 as an algebraic extension of @var{GF(2)} with the defining polynomial  as an algebraic extension of @var{GF(2)} with the defining polynomial
 @var{f mod 2}. In both cases the primality check of the argument is  @var{f mod 2}. Furthermore, finite extensions of prime finite fields
   can be defined. @xref{Types of numbers}.
   In all cases the primality check of the argument is
 not done and the caller is responsible for it.  not done and the caller is responsible for it.
   
 Correctly speaking there is no actual object corresponding to a 'base field'.  Correctly speaking there is no actual object corresponding to a 'base field'.
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